The Talmud (BT Berakhot 13a) [indicates its surprise that the name Ya’akov continues to be used, whereas] the biblical text seems to prohibit any further use of that name: And God said unto him: ‘Your name is Ya’akov: your name shall not be called any more Ya’akov, but Yisrael shall be your name’; and He called his name Yisrael (Gen. 35:10)… [It then answers,] “There is a difference in his case, because Scripture restored [the name Ya’akov] to him, as it is written (Gen. 36:2): And God spoke unto Yisrael in the visions of the night, and said, ‘Ya’akov, Ya’akov.'”
In essence, the Talmud doesn’t really answer the question. Rather, it appeals to authority by saying that in the case of Ya’akov the Torah itself reverts back to the older name – in which case we must assume that it is acceptable…
Perhaps the Talmud’s question can be answered [as follows]: Given our understanding of a name’s function as a description of a person’s essence, the prohibition is really a tautology: it is a logical proposition that since A (the essence described by the first name) is different than B (the essence described by the new name), A cannot describe B. Hence, if I receive a new name, it is axiomatic that I cannot keep my old name. To put it differently, if a name is meant to represent an identity, a person is entitled to only one. Unless, of course, a person can have more than one identity.
In actual fact, there is ample evidence to suggest that the existence of a double identity here is precisely what the Torah wants us to recognize. The careful reader will notice a constant and unique duality that exemplifies the life of Ya’akov and thereby makes him exceptional. His two (sets of) wives are only the beginning – if perhaps the most important indicator – of his double personality… The duality denoted by his very different wives is in turn institutionalized through the rivalry for leadership among their sons, primarily represented by Judah and his descendants on the one hand and Joseph and his descendants on the other. In the end, this rivalry and the different approaches represented by the two parts of Ya’akov-Yisrael may have been a very significant factor leading to, and reinforcing, the division of the Jewish nation into the northern (Ephraim) and the southern (Judah) kingdoms.
Similarly, Ya’akov’s usurpation of his twin Esau’s birthright and blessing can represent a taking on of Esau’s personality alongside his own. In this sense, the rabbinic tradition that the wrestler that Ya’akov subdues is actually Esau’s guardian angel fits in well. Ya’akov wants confirmation of his status as the true first born. This confirmation is best represented by his older brother’s guardian angel – so long as Esau still has his own angel, Ya’akov has not completely taken on Esau’s essence. Thus, the struggle at the Jabbok embodies the notion that, having taken on Esau’s role as the firstborn, he should now subdue Esau’s guardian angel in order to seek his protection (alongside that of his own original guardian angel).
Finally, there is a cluster of clues to this duality specifically around the narratives of Ya’akov receiving his new name (which, we by now might have predicted, occurs twice). The story is significantly prefaced by his visit to Mahanayim – the double camp (Gen. 32:3), and bracketed by his two visits to Bet El (Gen. 28 and 35). Moreover, Ya’akov’s preparation for his meeting with Esau includes the sending of two delegations and the division of his camps into two parts, so that if one is destroyed, the other will survive.4 Survival of a half is only conceivable if it is not wholly dependent on the other half, which should not be taken for granted in view of the later frequent comparison of a nation to one body requiring all of its parts.
The notion that Torah is specifically trying to make us notice Ya’akov’s unusual double personality also helps us understand some of the strange juxtapositions of the two names, such as when he strengthens himself to bless Joseph’s children (Gen. 48:2-3). Though he is by now Yisrael, the text tells us that he is also still Ya’akov even when he acts like the former. The same occurs in reverse when Ya’akov offers his parting words to Simon and Levi, telling them that his dislike of their militancy is not only true of Ya’akov but also of Yisrael (Gen. 49:7). Thus, though one personality will dominate at any given time, the other personality is always still with him.
Nor does the juxtaposition end with the Torah. It is to be found further in the Bible, especially in the Psalms (for example, 147:19), which makes repeated side-by-side use of the two names. In those cases, the text is referring to his progeny, showing that this duality did not end with the death of Ya’akov-Yisrael but is in fact transmitted to his descendants as well…
It may be suggested that if Ya’akov represents a more sheltered and passive approach to life embodied by his childhood, and Yisrael represents a bolder, confrontational approach embodied more in his later years, the reason for Ya’akov’s split personality may be rooted in his need to maintain the legacy of both his father and his grandfather – echoed by his appealing to the God of Abraham and the God of Isaac (Gen. 32:10). From this perspective, while Ya’akov’s youth resembles that of his passive and isolated[…] father, his adult life resembles the trials and tribulations of Abraham among the nations. In this sense, Abraham’s outgoing personality is also what Ya’akov took from his brother Esau which, as some have suggested, Isaac had hoped would have actually been embodied by Esau rather than Ya’akov… [Apparently then,] Ya’akov was fated to bequeath a dual legacy to his descendants, something for which he became uniquely (or shall we say dually) suited.